Asymptotic solution for non-linear stage of suspension-colloidal flow in porous media is developed. The expansion is performed behind the concentration front; the zero order approximation coincides with the short-time solution of the linearised system. Using the first order approximation allows significantly enhancing the validity time period for the analytical model if compared with the linearised solution, allowing using the long-term experimental breakthrough concentration history for the model adjustment. Laboratory injection tests for three size colloids are performed. The asymptotic solution is used to tune the model parameters from the breakthrough histories of two size particles; good quality of matching is observed. The breakthrough concentration history for the third size particles is compared with the prediction by the adjusted model; good quality prediction is observed. The above serves for validation of the asymptotic method for the model tuning and prediction of non-linear suspension-colloidal flow in porous media.